Phase lock technique for random signal analysis : an application to Moessbauer resonance

The spectral density of random signals obeying Poisson distribution is uniformly distributed over the frequency range determined by the time constant of the detecting devices. Various noise sources also obey the Poisson statistics. Therefore, a technique is proposed for using the a.c. doppler modulation whereby the doppler velocity modulation in the Moessbauer spectroscopy is transformed to #betta#-ray intensity modulation. With this a.c. modulation the instantaneous energy could be represented by E = Esub(o) + Esub(o) (Vsub(o)/c)(t/tsub(o)-1/2)+1/2Esub(m) sin#betta#sub(m)t, where the 2nd term represents the conventional doppler shift with the ramp type of velocity signal and the last term is due to a.c. modulation with the frequency #betta#sub(m) >>2π/tsub(o). The theoretical analysis of this new technique as to the shape of the resonance absorption and width of the resonance line etc. as a function of the depth of modulation is presented. It is shown that the Moessbauer absorption could be detected at the modulation frequency and reducing the background radiation which is uniformly distributed throughout the frequency range. Thus the application of the phase sensitive detection method greatly enhances the S/N ratio. (author)